For each edge insertion or deletion, a DEBI entry needs to be initialized or cleared. In addition, each update in the data graph may change the DEBI for many neighboring edges.
The effect propagates up to \(d\) -hop away from the initial edge, where \(d\)  is the diameter of the query graph.
Multiple iterations through this neighborhood are required before an equilibrium is reached and the minimal candidate set is obtained, which is shown to be NP-Hard [1]}. Mnemonic, similar to existing works, relies on single pass top-down and bottom-up filtering following the matching order. After the completion, this process verifies the duality of every candidate of each edge in the query tree. The matches for edges not in the query tree, that is, non-tree edges, are verified during enumeration.
